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REMARKS ON CONVERGENCE OF MORLEY SEQUENCES

Part of: Model theory

Published online by Cambridge University Press:  04 April 2023

KARIM KHANAKI Open the ORCID record for KARIM KHANAKI [Opens in a new window]
KARIM KHANAKI*
Affiliation:
DEPARTMENT OF SCIENCE ARAK UNIVERSITY OF TECHNOLOGY ARAK 3818146763, IRAN
*
E-mail: khanaki@arakut.ac.ir
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Abstract

We refine results of Gannon [6, Theorem 4.7] and Simon [22, Lemma 2.8] on convergence of Morley sequences. We then introduce the notion of eventual$NIP$, as a property of a model, and prove a variant of [15, Corollary 2.2]. Finally, we give new characterizations of generically stable types (for countable theories) and reinforce the main result of Pillay [17] on the model-theoretic meaning of Grothendieck’s double limit theorem.

Keywords

generic stabilityMorley sequenceGrothendieck’s double limit theoremeventual NIP

MSC classification

Primary: 03C45: Classification theory, stability and related concepts
Type
Article
Information
The Journal of Symbolic Logic , First View , pp. 1 - 19
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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Footnotes

Dedicated to the memory of my first teacher Fatemeh Mardani

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